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AP EAMCET · Maths · Probability

If \(X \sim B(5, p)\) is a binomial variate such that \(p(X=3)=\) \(p(X=4)\), then \(p(|X-3| \lt 2)=\)

  1. A \(\frac{242}{243}\)
  2. B \(\frac{201}{243}\)
  3. C \(\frac{200}{243}\)
  4. D \(\frac{121}{243}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{200}{243}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { } X \sim B(5, p) \\ & p(X=3)=p(X=4) \\ & \Rightarrow{ }^5 C_3 p^3(1-p)^2={ }^5 C_4 p^4(1-p) \\ & \Rightarrow 10(1-p)=5 p \Rightarrow p=\frac{10}{15}=\frac{2}{3} \\ & p(|X-3| \lt 2)=p(-2 \lt X-3 \lt 2)=p(1 \lt X \lt 5) \\ & =p(X=2)+p(X=3)+p(X=4)=p(X=2)+2…